(5n+6)(5n-5)=0

Solution for (5n+6)(5n-5)=0 equation:

Simplifying
(5n + 6)(5n + -5) = 0

Reorder the terms:
(6 + 5n)(5n + -5) = 0

Reorder the terms:
(6 + 5n)(-5 + 5n) = 0

Multiply (6 + 5n) * (-5 + 5n)
(6(-5 + 5n) + 5n * (-5 + 5n)) = 0
((-5 * 6 + 5n * 6) + 5n * (-5 + 5n)) = 0
((-30 + 30n) + 5n * (-5 + 5n)) = 0
(-30 + 30n + (-5 * 5n + 5n * 5n)) = 0
(-30 + 30n + (-25n + 25n2)) = 0

Combine like terms: 30n + -25n = 5n
(-30 + 5n + 25n2) = 0

Solving
-30 + 5n + 25n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + n + 5n2) = 0

Factor a trinomial.
5((-6 + -5n)(1 + -1n)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-6 + -5n)' equal to zero and attempt to solve:

Simplifying
-6 + -5n = 0

Solving
-6 + -5n = 0

Move all terms containing n to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + -5n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5n = 0 + 6
-5n = 0 + 6

Combine like terms: 0 + 6 = 6
-5n = 6

Divide each side by '-5'.
n = -1.2

Simplifying
n = -1.2
Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1n = 0 + -1
-1n = 0 + -1

Combine like terms: 0 + -1 = -1
-1n = -1

Divide each side by '-1'.
n = 1

Simplifying
n = 1
Solution
n = {-1.2, 1}